How did the court justify that conclusion over the more obvious conclusion that copyright—including of recordings—is governed by federal law with a constitutional requirement for time limits?
Current situation is not much better to be honest.
And since this is common law, why haven't any other courts given their own alternate common law? Deferring to English law is bizarre, considering that the Constitution was written specifically to replace English law, including a specific Copyright clause, and backed by a war against England.
The Constitution isn’t a legal system in and of itself. Rather it sets out a system of government and gives one branch the power to make laws, another to execute them and veto new ones, and a third to supervise and rule on those laws (including setting up a court system).
Err, I've got bad news for you about a lot of law.
By analogy, I could imagine a "Dormant Copyright Clause" doctrine, meaning that the states shouldn't have the power to legislate copyright other than in whatever contexts the Federal government explicitly leaves to them.
This is all theory, of course. But actual case law does say something at least similar. See for instance Sears, Roebuck & Co. v. Stiffel Co., a case in which the Supreme Court said (in the context of patents) that the Constitution reserves the power over them to the Federal Government exclusively, and that the states can't give patent protection to something that Federal law doesn't protect.
This is what Congress did when passed the ~1978 legislation (even if somewhat retroactively, based on your dormant commerce argument). It explicitly affirmed existing state law for previous recordings, while declaring exclusive Federal jurisdiction for the future.
"In 2005 the landmark case of Capitol v. Naxos pitted a distributor of 1930s foreign classical recordings (Naxos) against the putative holder of the U.S. rights to those recordings. The judges of the New York State Court of Appeals ruled against Naxos, but they used the opportunity to go much further than that. They declared that since New York State had not passed explicit statutes dealing with recording copyright, it was in fact governed by “common law” (i.e., law declared by judges in their rulings). In their opinion sound recording copyright in New York derived from the laws of seventeenth-century English kings. It was absolute and perpetual. The rights holders have all rights, forever, and the public has none." (Capitol Records, Inc., v. Naxos of America, Inc., 830 N.E. 2d 250 (N.Y. App. 2005).)
See: https://recordingcopyright.org/pdf/AMuscop_fnl.pdf
Therefore, it is illegal to copy and distribute an old recording of Rhapsody in Blue if the recording was made in the US.